Opposition Leader Bill Shorten has rebuked Stephen Conroy after the senator criticised the Governor-General in the Upper House this morning.

The Deputy Leader of the Opposition in the Senate said Sir Peter Cosgrove's decision to allow a special sitting of Parliament "demeaned his office" and invoked the dismissal of Gough Whitlam in 1975 in what he called a "travesty of democracy".

The remarks came as the Senate sat to debate the controversial ABCC bill, the rejection of which Prime Minister Malcolm Turnbull says he will use as a trigger to call a double dissolution election.

But Senator Conroy's fiery opening salvo has earned him a slap-down from Mr Shorten.

"The Governor-General has one of the most important roles in our democracy and that should be respected by everyone," Mr Shorten said this evening.

"This was intemperate and unnecessary. Senator Conroy should confine his remarks to the Government."

Mr Shorten's admonition came after the prime minister had called for Mr Conroy to be reprimanded for the "appalling remarks", which included a reference to the metaphorical zombie appendage of Australia's 18th governor-general.

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"The long, dead arm of Sir John Kerr crawled out of his grave to participate in a travesty of democracy in this country," Mr Conroy said this morning, adding that "if the Queen had been asked to interfere in the British Parliament in this way, there is no way on this Earth this would have happened”.

Sir Peter, meanwhile, created an awkward scene himself in the Lower House when he failed to shake hands with Labor Deputy Tanya Plibersek.

This evening the Senate voted down the bill reintroduce the office of the Australian Building and Construction Commission.